On the M/G/1 queue with quadratic repeated attempts

Abstract

Single server queues with repeated attempts arise naturally in computer and telecommunication systems. The increasing interest on this topic is mainly explained by the development of new technological facilities such as “repeat last number”, “repeat a fixed number of times”, “ring back when free”, etc. In this paper we analyze an M/G/1 queue operating under a quadratic retrial policy. The consideration of a quadratic policy extends the existing literature and provides more flexibility to the queueing design. When the service time distribution is exponential we show that the main performances measures can be expressed in terms of hypergeometric functions. The case of general service times is investigated with the help of a regenerative approach.